# Three circles each of radius 3.5 cm are drawn in such a way that each of them touches the other two. Find the area enclosed between these circles. - Mathematics

Sum

Three circles each of radius 3.5 cm are drawn in such a way that each of them touches the other two. Find the area enclosed between these circles.

#### Solution

The three circles are drawn in such a way that each of them touches the other two.

So, by joining the centers of the three circles, we get,

AB = BC = CA = 2(Radius) = 7 cm

Therefore, triangle ABC is an equilateral triangle with each side 7 cm.

∴ Area of the triangle = (sqrt(3)/4) xx a^2

Where a is the side of the triangle.

= (sqrt(3)/4) xx (7)^2

= 49/9 sqrt(3) cm^2

= 21.2176 cm2

Now, Central angle of each sector =  = 60° ((60π)/180)

= pi/3 radians

Thus, area of each sector = (1/2) r2θ

= (1/2) xx (3.5)^2 xx (pi/3)

= 12.25 xx 22/(7 xx 6)

= 6.4167 cm2

Total area of three sectors = 3 × 6.4167 = 19.25 cm2

∴ Area enclosed between three circles = Area of triangle ABC – Area of the three sectors

= 21.2176 – 19.25

= 1.9676 cm2

Hence, the required area enclosed between these circles is 1.967 cm2 (approx.).

Concept: Areas of Sector and Segment of a Circle
Is there an error in this question or solution?

#### APPEARS IN

NCERT Mathematics Exemplar Class 10
Chapter 11 Area Related To Circles
Exercise 11.4 | Q 7 | Page 133
Share